Meaning, I bottled my beer a few weeks ago, and I tried one the other day and it tasted great. Should I just throw all my beers in the fridge now? Or could I keep letting them ferment in room temp? Is there a bad part to letting them just sit in my closet, not fridged? What is happening to the beer?

Leave them. Unless you're talking about years (which is crazy, how do you not drink it) the beer will be fine. There's no need to throw all of the bottles in the fridge. Just keep them out of sunlight and at a constant-ish temperature as you would get in a garage, basement, closet, wherever.

Eventually the yeasties will have nothing left to eat and will settle to the bottom. I don't know chemically what's happening to the beer, but your beer will taste different at one month and six months. Not worse, usually better.

Really depends on what style of beer you made. But, for most brews it takes months (if not years), before they start to go south. In most cases they get better with age. And tmags, I have some bottles downstairs on the shelf that are at least 2 years old. I still sample them on occasion. Some beers can hold their own with aging, but surely not all. Cheers!!!

Some styles are gonna taste great right after they carb up; think wheats, kolsch's, cream ales, etc. IPA's or hoppy pale ales are sometimes in this category as the hop aromas and flavors will dissapate with time. But you have 2 months probably where they are at their peak.

Some are going to taste better after they cellar or age at room temp; think belgian tripels, russian imperial stouts, barleywines, etc. These will age better at cellar or cool room temps than in the fridge. Just a faster process.

Some are going to tast better if they get extended fridge time to lager.

I don't think there's one set answer as it really depends on what you brewed.